How can I create a 2-D texture of green clouds on a black background?
In your shader editor, I would suggest something along the lines of this:

That's a Noise Texture, generally Perlin, taken to an adjustable power with an adjustable factor added to it, used to mix RGB between jet black and glowing green. Then, it's attached to the color of an emission shader, with an adjustable strength (I went with 4.6), and finally tied to the surface output. You can play with the power and the addition to bias your clouds toward green or black, and change the contrast.
This would work equally well as a world shader, if you're going for a background instead. You could also use the noise output to mix the emission with a transparency shader (Mix Shader) to have a clear background, if you needed to. Have fun!